Least‐Resistance Path as a Proxy for Efficient Simulation of Solute Transport in Heterogeneous Porous Media

Abstract Accurately predicting solute transport remains a central challenge in hydrogeology due to limited data and multiscale subsurface heterogeneity. Fractional Brownian motion (fBm) is widely used to model the logarithm of hydraulic conductivity fields. We introduce an exact and computationally efficient approach for simulating fBm‐based lognormal conductivity fields and use it to examine the relationship between the fastest path (FP) and the least‐resistance path (LRP). Our results show that the LRP provides a robust approximation of the FP and accurately predicts first‐arrival times in heterogeneous media. Travel time along the LRP is computed by integrating the inverse of the velocity component projected along the path. Because identifying the FP requires full particle tracking, whereas LRP‐based travel times require only the flow field, the LRP provides a practical and physically meaningful proxy for solute transport in highly heterogeneous porous formations.